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On the differential structure of metric measure spaces and applications /
"The main goals of this paper are: (i) To develop an abstract differential calculus on metric measure spaces by investigating the duality relations between differentials and gradients of Sobolev functions. This will be achieved without calling into play any sort of analysis in charts, our assum...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, Rhode Island :
American Mathematical Society,
2015.
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| Colección: | Memoirs of the American Mathematical Society ;
no. 1113. |
| Temas: | |
| Acceso en línea: | Texto completo |
| Sumario: | "The main goals of this paper are: (i) To develop an abstract differential calculus on metric measure spaces by investigating the duality relations between differentials and gradients of Sobolev functions. This will be achieved without calling into play any sort of analysis in charts, our assumptions being: the metric space is complete and separable and the measure is Radon and non-negative. (ii) To employ these notions of calculus to provide, via integration by parts, a general definition of distributional Laplacian ... (iii) To show that on spaces with Ricci curvature bounded from below and dimension bounded from above, the Laplacian of the distance function is always a measure and that this measure has the standard sharp comparison properties. This result requires an additional assumption on the space, which reduces to strict convexity of the norm in the case of smooth Finsler structures and is always satisfied on spaces with linear Laplacian, a situation which is analyzed in detail."--Page v |
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| Notas: | "Volume 236, number 1113 (third of 6 numbers), July 2015." |
| Descripción Física: | 1 online resource (v, 91 pages) |
| Bibliografía: | Includes bibliographical references (pages 89-91). |
| ISBN: | 9781470422790 1470422794 |
| ISSN: | 1947-6221 ; |